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arXiv:physics/0604088 · Physical Review A

Dependence of fluorescence-level statistics on bin-time size in a few-atom magneto-optical trap

Sungsam Kang, Seokchan Yoon, Youngwoon Choi, Jai-Hyung Lee, Kyungwon An

Published Jul 24, 2006• 6 citations
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Abstract

We have analyzed the statistical distribution of the fluorescence signal levels in a magneto-optical trap containing a few atoms and observed that it strongly depends on the relative size of the bin time with respect to the trap decay time. We derived analytic expressions for the signal distributions in two limiting cases, long and short bin time limits, and found good agreement with numerical simulations performed regardless of the size of the bin time. We found an optimal size of the bin time for minimizing the probability of indeterminate atom numbers while providing accurate information on the instantaneous number of atoms in the trap. These theoretical results are compared with actual experimental data. We observed super-Poisson counting statistics for the fluorescence from trapped atoms, which might be attributed to uncorrelated motion of trapped atoms in the inhomogeneous magnetic field in the trap.

DOI
10.1103/physreva.74.013409

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We have analyzed the statistical distribution of the fluorescence signal levels in a magneto-optical trap containing a few atoms and observed that it strongly depends on the relative size of the bin time with respect to the trap decay time. We derived analytic expressions for the signal distributions in two limiting cases, long and short bin time limits, and found good agreement with numerical simulations performed regardless of the size of the bin time. We found an optimal size of the bin time for minimizing the probability of indeterminate atom numbers while providing accurate information on the instantaneous number of atoms in the trap. These theoretical results are compared with actual experimental data. We observed super-Poisson counting statistics for the fluorescence from trapped atoms, which might be attributed to uncorrelated motion of trapped atoms in the inhomogeneous magnetic field in the trap.
A quantitative study on characteristics of a magneto-optical trap with a single or a few atoms is presented. A very small number of 85 Rb atoms were trapped in a micron-size magneto-optical trap with a high magnetic-field gradient. In order to find the optimum condition for a single-atom trap, we have investigated how the number of atoms and the size of atomic cloud change as various experimental parameters, such as a magnetic-field gradient and the trapping laser intensity and detuning. The averaged number of atoms was measured very accurately with a calibration procedure based on the single-atom saturation curve of resonance fluorescence. In addition, the number of atoms in a trap could be controlled by suppressing stochastic loading events by means of a real-time active feedback on the magnetic-field gradient.
Our study indicates that the number of trapped Rb atoms in a magneto-optical trap (MOT) strongly depends on the trapping laser intensity and detuning, the repumping laser intensity and the magnetic gradient. We estimate the trapped-atom numbers changing with the trapping laser intensity and detuning, using a two-level system model. The theoretical results are in qualitative agreement with the experimental results. The experimental results also show an obvious dependence of the trapped-atom numbers on repumping laser intensity and the magnetic gradient, which the simple theory cannot account for. These studies are helpful for selecting suitable experimental parameters to achieve larger numbers of cold atoms.
In our experiment, firstly, we carry out the loading of single atoms in the magneto-optical trap (MOT) by increasing the quadrupole magnetic field gradient, improving the background vacuum, and reducing the diameters of the cooling and trapping laser beams. Secondly, we get the single atomic fluorescence signal of a high signal-to-background ratio in the MOT by means of reducing the detuning of cooling light and increasing its intensity appropriately, and using the polarization spectroscopy locking technique to suppress the fluctuations of cooling laser. In addition, with the real-time feedback on quadrupole magnetic field gradient, we demonstrate a probability of loading single atoms in the MOT as high as 98%. We also measure the statistical properties of the single atomic fluorescence which is excited by continuous light in the MOT; the measured second-order correlation is g(2)( = 0) = 0.09.
The theoretical description of the external degrees of freedom of atoms trapped inside a magneto-optical trap (MOT) often relies on the decoupling of the evolution of the internal and external degrees of freedom. That is possible thanks to much shorter timescales typically associated with the first ones. The electronic structure of alkaline-earth atoms, on the other hand, presents ultra-narrow transitions and metastable states that makes such an approximation invalid in the general case. In this article, we report on a model based on open Bloch equations for the evolution of the number of atoms in a magneto-optical trap. With this model we investigate the loading of the strontium blue magneto-optical trap under different repumping schemes, either directly from a Zeeman slower, or from an atomic reservoir made of atoms in a metastable state trapped in the magnetic quadrupolar field. The fluorescence observed on the strong 461~nm transition is recorded and quantitatively compared with the results from our simulations. The comparison between experimental results and calculations within our model allowed to identify the existence of the decay paths between the upper level of the repumping transition and the dark strontium metastable states, which could not be explained by electric dipole transition rates calculated in the literature. Moreover, our analysis pinpoints the role of the atomic movement in limiting the efficiency of the atomic repumping of the Sr metastable states.
We report fluorescence detection of a single 7 Li atom in a magneto-optical trap (MOT). We use a double MOT system, which allows us to control the loading rate of the second MOT by simply turning on or off the first MOT and to use a modest magnetic field gradient of 46 G/cm. A single atom is trapped for longer than 100 s. The fluorescence from the trapped atoms is imaged onto an electron-multiplying charge-coupled device with a unit magnification factor by a pair of aspheric lenses. The numerical aperture of the objective lens is 0.22 with a collecting efficiency of 1.3%. Accumulated fluorescence is extracted by integrating the signal over a region of interest of 500×350 μ m 2 . For a 200-ms exposure time, the fluorescence count from a single atom is 8.8×10 3 and the background count from scattered MOT beams is 6.8 × 10 4 . We actively stabilize the trap beam power to reduce the noise and the measured noise is two times the statistical noise. Overall signal-to-noise ratio of the single-atom detection is 37/√ Hz. We also describe a modification of the system that is adapted to an experimental configuration for quantum manipulation of single atoms in a 1D optical lattice.